Find the x and y Intercepts y=((2x-2)(x+2))/((4x+4)(2x+1))

$y = \frac{(2 x - 2) (x + 2)}{(4 x + 4) (2 x + 1)}$

Step 1

Find the x-intercepts.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{(2 x - 2) (x + 2)}{(4 x + 4) (2 x + 1)}$

Solve the equation.

Set the numerator equal to zero.

$(2 x - 2) (x + 2) = 0$

Solve the equation for $x$ .

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$2 x - 2 = 0$

$x + 2 = 0$

Set $2 x - 2$ equal to $0$ and solve for $x$ .

Set $2 x - 2$ equal to $0$ .

$2 x - 2 = 0$

Solve $2 x - 2 = 0$ for $x$ .

Add $2$ to both sides of the equation.

$2 x = 2$

Divide each term in $2 x = 2$ by $2$ and simplify.

Divide each term in $2 x = 2$ by $2$ .

$\frac{2 x}{2} = \frac{2}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{2}{2}$

Divide $x$ by $1$ .

$x = \frac{2}{2}$

Simplify the right side.

Divide $2$ by $2$ .

$x = 1$

Set $x + 2$ equal to $0$ and solve for $x$ .

Set $x + 2$ equal to $0$ .

$x + 2 = 0$

Subtract $2$ from both sides of the equation.

$x = - 2$

The final solution is all the values that make $(2 x - 2) (x + 2) = 0$ true.

$x = 1, - 2$

x-intercept(s) in point form.

x-intercept(s): $(1, 0), (- 2, 0)$

Step 2

Find the y-intercepts.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{(2 (0) - 2) ((0) + 2)}{(4 (0) + 4) (2 (0) + 1)}$

Solve the equation.

Remove parentheses.

$y = \frac{(2 (0) - 2) (0 + 2)}{(4 (0) + 4) (2 (0) + 1)}$

Remove parentheses.

$y = \frac{(2 (0) - 2) ((0) + 2)}{(4 (0) + 4) (2 (0) + 1)}$

Simplify $\frac{(2 (0) - 2) ((0) + 2)}{(4 (0) + 4) (2 (0) + 1)}$ .

Reduce the expression by cancelling the common factors.

Cancel the common factor of $(0) + 2$ and $4 (0) + 4$ .

Factor $2$ out of $(2 (0) - 2) ((0) + 2)$ .

$y = \frac{2 ((0 - 1) ((0) + 2))}{(4 (0) + 4) (2 (0) + 1)}$

Cancel the common factors.

Factor $2$ out of $(4 (0) + 4) (2 (0) + 1)$ .

$y = \frac{2 ((0 - 1) ((0) + 2))}{2 ((2 \cdot 0 + 2) (2 (0) + 1))}$

Cancel the common factor.

$y = \frac{2 ((0 - 1) ((0) + 2))}{2 ((2 \cdot 0 + 2) (2 (0) + 1))}$

Rewrite the expression.

$y = \frac{(0 - 1) ((0) + 2)}{(2 \cdot 0 + 2) (2 (0) + 1)}$

Cancel the common factor of $(0) + 2$ and $2 \cdot 0 + 2$ .

Factor $2$ out of $(0 - 1) ((0) + 2)$ .

$y = \frac{2 ((0 - 1) (0 + 1))}{(2 \cdot 0 + 2) (2 (0) + 1)}$

Cancel the common factors.

Factor $2$ out of $(2 \cdot 0 + 2) (2 (0) + 1)$ .

$y = \frac{2 ((0 - 1) (0 + 1))}{2 ((0 + 1) (2 (0) + 1))}$

Cancel the common factor.

$y = \frac{2 ((0 - 1) (0 + 1))}{2 ((0 + 1) (2 (0) + 1))}$

Rewrite the expression.

$y = \frac{(0 - 1) (0 + 1)}{(0 + 1) (2 (0) + 1)}$

Cancel the common factor of $0 + 1$ .

Cancel the common factor.

$y = \frac{(0 - 1) (0 + 1)}{(0 + 1) (2 (0) + 1)}$

Rewrite the expression.

$y = \frac{0 - 1}{2 (0) + 1}$

Subtract $1$ from $0$ .

$y = \frac{- 1}{2 (0) + 1}$

Simplify the denominator.

Multiply $2$ by $0$ .

$y = \frac{- 1}{0 + 1}$

Add $0$ and $1$ .

$y = \frac{- 1}{1}$

Divide $- 1$ by $1$ .

$y = - 1$

y-intercept(s) in point form.

y-intercept(s): $(0, - 1)$

Step 3

List the intersections.

x-intercept(s): $(1, 0), (- 2, 0)$

y-intercept(s): $(0, - 1)$

Step 4

Find the x and y Intercepts y=((2x-2)(x+2))/((4x+4)(2x+1))

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